Viewing the simulation empirically:  The left brain

The previous simulation allowed you to watch how rapidly differently sized populations diffused from one compartment into another, to reach equilibrium. Did you formulate an hypothesis about what factors affected their velocity? Was the rate faster if there were absolutely more particles in the left-hand compartment? Or was the rate more a function of the differences in concentration? Could you tell?

This simulation allows you to change the number of particles in the left-hand compartment, which has volume of 50 units, and to plot the rates of diffusion as a function of the concentration gradient (dC), the difference in particle concentrations in the two compartments. A positive rate indicates more particles are moving from left to right; more particles are moving from right to left when the rate is negative.

From the left, the first button in the control panel at the bottom of the simulation starts or stops the simulation; the second sets the initial particle concentration; the next starts or stops the plotting function; the fourth generates a function relating all the data plotted for any initial concentration setting; "FitTot" generates the best linear function for all the data plotted; and the last button resets the simulation.

How does the rate change as the particles reach an equilibrium distribution between the two compartments? Do the individual plots represent intuitively reasonable relationships between R and dC? Is the plot generated by "FitTot" a better indicator of the relationship than those produced by the individual plots? Why or why not? Why is there so much data scatter?

Note the equation generated by plotting function is of the form of a linear equation - Y = b + aX - where Y is R, X is dC and a and b are constants. What should be value of "b" be? What is "a"? Run the simulations several times, collate your data and compare them with those collected by other students. Then consider the background material presented in the adjacent column.

 Viewing the simulation theoretically:  The right brain

In the middle of the last century, the German physiologist Fick applied the principles of heat conduction to various examples of diffusion in animals. He observed that the velocity at which a substance diffused through a given cross sectional area, its diffusive flux (J), was related to the concentration gradient of that substance (dC/dX), in the following manner:

J = D(dC/dX)

where D is the Diffusion coefficient (in cm2 per sec). Integrating this expression produces the following relationship:

J = D(DC)/X

Thus, in the cgs system, a DC (deltaC) measured in M (mol per l or mmol per cm3) over a distance of 1 cm, with a Diffusion Coefficient in cm2 per sec, would produce a J with units of (mol per cm2) per sec. Redefining the terms and solving for the substance's rate (R) of diffusion produces:

R = PA (DC)

where P is the Permeability Coefficient of the substance being measured (the Diffusion Coefficient per unit X), and A is the effective cross-sectional area of the region over which diffusion occurs. This is the usual form of the Fick Equation.

What particle or membrane parameters would affect the magnitude of D? and in what direction? Would you expect a charged particle to move more rapidly across a membrane than an uncharged one? Should all membranes exhibit the same D's for the same substances? Suppose they don't...? Suppose the R for a given membrane permeant is not a linear function of dC, what then?

Historically, testing the validity of the Fick equation has allowed physiologists to determine whether transport is driven strictly by diffusion or whether "facilitated" mechanisms, such as active transport must be postulated.